F. K. Kong MA, MSc, PhD, CEng, FICE, FIStructE, R. H. Evans CBE, DSc, D ès Sc, DTech, PhD, CEng, FICE, FIMechE, FIStructE (auth.)-Reinforced and Prestressed Concrete-Springer US (1987)

Statistical concepts 3
occur in practice in the loads acting on the structure or in the strength of
the materials. Before further discussion of limit state design, it is desirable,
therefore, to review some relevant concepts in statistics.
1.3 Statistical concepts
In this section we shall briefly discuss those concepts of statistics which are
helpful to our study of limit state design philosophy. For more detailed
descriptions of statistical methods and of the theory underlying them, the
reader is referred to other specialist texts [8, 9].
Probability
Suppose there is a large number n of occasions on which a certain event is
equally likely to happen, and that the event happens on a number m of the
n occasions. We then say that the probability of the event happening on
any one of then occasions is min, and the probability of its not happening
on any one of then occasions is 1 - min. Probability is thus expressed as a
number not greater than 1. A value of unity denotes a certainty of the
event happening; a value of zero means an impossibility of the event
happening. (Note: We have adopted the above concept of probability
because it serves our purpose and its meaning is intuitively clear, at least to
structural engineers. However, it should be pointed out that some
mathematicians [10] regard this concept as invalid and meaningless.)
Frequency distribution
Table 1.3-1 gives the results of cylinder splitting tensile tests on 100
concrete specimens. The numbers in the table are called the characteristic
values of the variate; in this case the variate is the tensile strength. The
characteristic values can be studied more conveniently if they are
rearranged in ascending order of magnitude. Since the numbers are correct
to one decimal place, a value of 2.1, for example, may represent any value
from 2.05 to 2.14. In Table 1.3-2, the characteristic values are divided into
class intervals of 1.45-1.54, 1.55-1.64 ... and 2.65-2.74, and the number
of values falling into each interval, known as the frequency in the interval,
is also shown. Table 1.3-2, therefore, shows the frequency distribution of
the tensile strengths, since it shows with what frequencies tensile strengths
Table 1.3-1 Tensile strengths of concrete (N/mm 2 )
2.1 1.9 2.2 2.5 2.0 1.8 1.9 2.0 2.2 2.0
2.2 1.7 2.0 2.4 1.8 1.9 2.0 1.5 2.4 2.1
2.6 2.0 2.3 2.0 1.7 2.0 2.2 1.5 2.4 2.0
1.8 1.6 2.3 2.0 2.2 2.0 2.2 1.8 2.1 2.2
2.3 1.9 1.8 2.2 1.8 1.7 2.2 1.6 2.7 2.3
1.6 1.8 1.9 2.5 1.9 1.9 2.0 1.7 1.7 2.0
1.8 1.7 2.2 1.7 2.1 2.4 1.9 1.9 2.0 2.0
2.0 2.2 1.9 2.1 2.0 2.4 2.0 2.0 1.8 2.1
1.8 1.7 2.3 1.8 2.0 2.4 1.8 2.0 1.8 2.2
1.9 1.8 2.0 1.6 1.8 2.3 2.5 1.7 2.3 2.0